I'm going to fly to St. Louis for christmas this year, but my flight leaves out of SJC at 6:30 AM. I'm in San Francisco and my dad doesn't even have a license. Are there any transit services that can get me to SJC by 5 AM?

Do you know the way to San Jose?
I've been away so long. I may go wrong and lose my way.
Do you know the way to San Jose?
I'm going back to find some peace of mind in San Jose.
L.A. is a great big freeway.
Put a hundred down and buy a car.
In a week, maybe two, they'll make you a star
Weeks turn into years. How quck they pass
And all the stars that never were
Are parking cars and pumping gas
Do you know the way to San Jose?
They've got a lot of space.There'll be a place where I can stay
I was born and raised in San Jose
I'm going back to find some peace of mind in San Jose.
Fame and fortune is a magnet.
It can pull you far away from home
With a dream in your heart you're never alone.
Dreams turn into dust and blow away
And there you are without a friend
You pack your car and ride away
I've got lots of friends in San Jose
Do you know the way to San Jose?
Can't wait to get back to San Jose.

The South Bay Flyer that was mentioned wont work. The earliest arrival to SJC is at 7:45 AM. That's waaayyy too late for me.

I also checked the SJC website and they don't have a lot of information regarding transit. Looks like I may either have to take a cab and pay a rediculous amount of money or try to find another flight.